In [1]:
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import plotly.express as px
import statsmodels.api as sm
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from statsmodels.tsa.stattools import grangercausalitytests
from statsmodels.tsa.stattools import coint
import scipy
from itertools import permutations
In [2]:
def calculate_ols_trendline(y_values):
x_values = np.arange(len(y_values))
x_values = sm.add_constant(x_values)
model = sm.OLS(y_values, x_values, missing='drop').fit()
trendline = model.predict(x_values)
return trendline
In [3]:
def test_granger_causality(data_frame, column1, column2, max_lags=5):
# Replace inf values with NaN and drop rows with NaN values
data_frame = data_frame[[column1, column2]].replace([np.inf, -np.inf], np.nan).dropna()
# Perform the Granger causality test
test_result = grangercausalitytests(data_frame[[column1, column2]],max_lags, verbose=False)
print("Granger Causality Test Results:\n")
for lag in range(1, max_lags+1):
f_test = test_result[lag][0]['ssr_ftest']
chi2_test = test_result[lag][0]['ssr_chi2test']
lr_test = test_result[lag][0]['lrtest']
params_ftest = test_result[lag][0]['params_ftest']
print(f"Lag {lag}:")
print(f" F-test: Statistic = {f_test[0]}, P-value = {f_test[1]}")
print(f" Chi-squared test: Statistic = {chi2_test[0]}, P-value = {chi2_test[1]}")
print(f" Likelihood-ratio test: Statistic = {lr_test[0]}, P-value = {lr_test[1]}")
print(f" Params F-test: Statistic = {params_ftest[0]}, P-value = {params_ftest[1]}\n")
return test_result
In [4]:
from itertools import permutations
import pandas as pd
def test_all_pairs_granger_causality(data_frame, max_lags=5):
results = []
columns = data_frame.columns
for col1, col2 in permutations(columns, 2):
data = data_frame[[col1, col2]].replace([np.inf, -np.inf], np.nan).dropna()
test_result = grangercausalitytests(data, max_lags, verbose=False)
for lag in range(1, max_lags+1):
f_test = test_result[lag][0]['ssr_ftest']
result = {
'Causality Vallues': f'{col1}/{col2}',
'Lag': lag,
'F-Statistic': f_test[0],
'P-value': f_test[1],
'Significant': 'Yes' if f_test[1] < 0.05 else 'No'
}
results.append(result)
granger_results_df = pd.DataFrame(results)
return granger_results_df
In [5]:
def t_test(data_frame, column1, column2, equal_var=False):
# Replace inf values with NaN and drop rows with NaN values
data_frame = data_frame[[column1, column2]].replace([np.inf, -np.inf], np.nan).dropna()
f_statistic, p_value = scipy.stats.ttest_ind(data_frame[column1], data_frame[column2])
if p_value < 0.05:
print("There is a significant difference between the groups.")
else:
print("No significant difference found between the groups.")
return f_statistic, p_value
In [6]:
def test_levene(data_frame, column1, column2):
# Replace inf values with NaN and drop rows with NaN values
data_frame = data_frame[[column1, column2]].replace([np.inf, -np.inf], np.nan).dropna()
# Perform the levene test
f_statistic, p_value = scipy.stats.levene(data_frame[column1], data_frame[column2] , center='median', proportiontocut=0.05)
print(f"Levene Test F-statistic: {f_statistic}")
print(f"P-value: {p_value}")
if p_value < 0.05:
print("There is a significant difference between the groups.")
else:
print("No significant difference found between the groups.")
return f_statistic, p_value
In [7]:
def test_anova(data_frame, columns,use_var='unequal',welch_correction=True):
data_frame = data_frame[columns].replace([np.inf, -np.inf], np.nan).dropna()
groups = [data_frame[col] for col in columns]
f_statistic, p_value = scipy.stats.f_oneway(*groups)
print(f"ANOVA Test F-statistic: {f_statistic}")
print(f"P-value: {p_value}")
if p_value < 0.05:
print("There is a significant difference between the groups.")
else:
print("No significant difference found between the groups.")
return f_statistic, p_value
In [8]:
def test_coint(data_frame, column1, column2):
# Replace inf values with NaN and drop rows with NaN values
data_frame = data_frame[[column1, column2]].replace([np.inf, -np.inf], np.nan).dropna()
# Perform the Cointegration test
score, p_value, crit_values = coint(data_frame[column1], data_frame[column2])
print(f"Cointegration Test Statistic: {score}")
print(f"P-value: {p_value}")
if p_value < 0.05:
print("The series are likely cointegrated.")
else:
print("No evidence of cointegration.")
return score, p_value, crit_values
In [9]:
def test_all_pairs_coint(data_frame):
results = []
columns = data_frame.columns
for col1, col2 in permutations(columns, 2):
data = data_frame[[col1, col2]].replace([np.inf, -np.inf], np.nan).dropna()
if col1 == col2:
continue
else:
score, p_value, crit_values = test_coint(data_frame, col1, col2)
result = {
'Score': f'{col1}/{col2}',
'Test Statistic': score,
'P-value': p_value,
'Cointegrated': 'Yes' if p_value < 0.05 else 'No'
}
results.append(result)
coint_matrix = pd.DataFrame(results)
return coint_matrix
Data set import and cleaning
In [10]:
euro = pd.read_csv('euro 5 years.csv')
bitcoin = pd.read_csv('BTC-USD 5 years.csv')
etherium = pd.read_csv('ETH-USD 5 years.csv')
sp = pd.read_csv('S&P 500 (SPX) Historical Data NASDAQ.csv')
cac = pd.read_csv('cac 40 5 years.csv')
fts = pd.read_csv('FTSE 100 5 years.csv')
pound = pd.read_csv('GBP_USD 5 years.csv')
In [11]:
fts[['Open', 'High', 'Low']] = fts[['Open', 'High', 'Low']].replace(',', '', regex=True).astype('float64')
cac[['Open', 'High', 'Low']] = cac[[' Open', ' High', ' Low']].replace(',', '', regex=True).astype('float64')
Function : convert same format Date, calculate the mean, concact the mean vallue in a new Data Frame and replace the NaN with linar interpolation methode
In [12]:
def process_dataframes(dataframes, date_formats):
processed_dataframes = {}
for name, df in dataframes.items():
#Convert the Data set in same format and thest the Date in index
df['Date'] = pd.to_datetime(df['Date'], format=date_formats.get(name), errors='coerce')
df.set_index('Date', inplace=True)
# Calculate mean prices
mean_col_name = f'Mean Price {name.capitalize()}'
df[mean_col_name] = df[['Open', 'High', 'Low']].mean(axis=1)
processed_dataframes[name] = df[mean_col_name]
# Concatenate mean prices in new DataFrame
all_data_mean = pd.concat(processed_dataframes.values(), axis=1)
all_data_mean.columns = processed_dataframes.keys()
#Convert CAC 40 and FTSE 100 in dolars and replace the actual vallue
all_data_mean['cac'] = all_data_mean['cac'] * all_data_mean['euro']
all_data_mean['fts'] = all_data_mean['fts'] * all_data_mean['pound']
#Remove the remplace vallue with interpolate function
all_data_mean = all_data_mean[all_data_mean.columns].interpolate(method= 'linear' )
return all_data_mean
dataframes = {'euro': euro, 'bitcoin': bitcoin, 'etherium': etherium, 'fts': fts, 'pound': pound,
'sp': sp, 'cac': cac}
date_formats = {'euro': None, 'bitcoint': None, 'etherium': None, 'fts': '%d/%m/%Y',
'pound': '%d/%m/%Y', 'sp': '%m/%d/%Y', 'cac': '%m/%d/%y'}
all_data_mean = process_dataframes(dataframes, date_formats)
In [13]:
all_data_mean.columns
Out[13]:
Index(['euro', 'bitcoin', 'etherium', 'fts', 'pound', 'sp', 'cac'], dtype='object')
In [14]:
all_data_mean.info()
<class 'pandas.core.frame.DataFrame'> DatetimeIndex: 1891 entries, 2018-09-12 to 2023-12-11 Data columns (total 7 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 euro 1827 non-null float64 1 bitcoin 1827 non-null float64 2 etherium 1827 non-null float64 3 fts 1827 non-null float64 4 pound 1827 non-null float64 5 sp 1830 non-null float64 6 cac 1827 non-null float64 dtypes: float64(7) memory usage: 118.2 KB
Bitcoint/Etherium analyse¶
In [15]:
all_data_mean[['bitcoin', 'etherium']].corr(method= 'spearman')
Out[15]:
| bitcoin | etherium | |
|---|---|---|
| bitcoin | 1.000000 | 0.953484 |
| etherium | 0.953484 | 1.000000 |
In [16]:
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(20, 15), sharex=False)
# Plot the mean price of Bitcoin
all_data_mean['bitcoin'].plot(ax=ax1, fontsize=16, color='blue')
ax1.set_ylabel('Mean Price Bitcoin')
ax1.set_title('Mean Prices of Bitcoin and Ethereum with Rolling Correlation')
# Plot the mean price of Ethereum
all_data_mean['etherium'].plot(ax=ax2, fontsize=16, color='orange')
ax2.set_ylabel('Mean Price Ethereum')
# Calculate and plot the rolling correlation in the third subplot
rolling_corr = all_data_mean['etherium'].rolling(30).corr(all_data_mean['bitcoin'])
rolling_corr.plot(ax=ax3, fontsize=16, color='green')
ax3.set_ylabel('Rolling Correlation')
ax3.axhline(y=0, color='red', linestyle='--', linewidth=2)
# Add legend to the third subplot
ax1.legend(['Bitcoin Mean Price'])
ax2.legend(['Bitcoin Mean Etherium'])
ax3.legend(['Rolling Correlation BTC/ETH'])
# Use the seaborn style
plt.style.use('seaborn-v0_8-colorblind')
plt.savefig('bitcoin_etheriun.jpeg')
# Show the plots
plt.show()
Make the Granger Causality score beetwenn Bitcoin and Ehterium
In [17]:
test_granger_causality(all_data_mean, 'bitcoin', 'etherium', max_lags=5)
Granger Causality Test Results: Lag 1: F-test: Statistic = 20.47931250867985, P-value = 6.417180591997906e-06 Chi-squared test: Statistic = 20.513014065194408, P-value = 5.922719066664915e-06 Likelihood-ratio test: Statistic = 20.398649686034332, P-value = 6.2874143889837596e-06 Params F-test: Statistic = 20.479312508695152, P-value = 6.417180591948046e-06 Lag 2: F-test: Statistic = 11.217305932888081, P-value = 1.4393517271063477e-05 Chi-squared test: Statistic = 22.496245414857967, P-value = 1.3031739092009448e-05 Likelihood-ratio test: Statistic = 22.358722057273553, P-value = 1.395934992576251e-05 Params F-test: Statistic = 11.217305932889026, P-value = 1.4393517271049108e-05 Lag 3: F-test: Statistic = 10.03932170550651, P-value = 1.4631471854955786e-06 Chi-squared test: Statistic = 30.233994701448328, P-value = 1.2321700321788243e-06 Likelihood-ratio test: Statistic = 29.98615554979915, P-value = 1.3893420550221234e-06 Params F-test: Statistic = 10.039321705508376, P-value = 1.4631471854918153e-06 Lag 4: F-test: Statistic = 6.938798500217844, P-value = 1.5313121221361458e-05 Chi-squared test: Statistic = 27.89289893251848, P-value = 1.3112092151438257e-05 Likelihood-ratio test: Statistic = 27.681662576447707, P-value = 1.4469768221310347e-05 Params F-test: Statistic = 6.938798500217278, P-value = 1.5313121221377616e-05 Lag 5: F-test: Statistic = 5.6521512378289955, P-value = 3.533789083992374e-05 Chi-squared test: Statistic = 28.432411803767064, P-value = 2.9956599752444827e-05 Likelihood-ratio test: Statistic = 28.212848370159918, P-value = 3.307219407698228e-05 Params F-test: Statistic = 5.652151237829557, P-value = 3.533789083988168e-05
/Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results warnings.warn(
Out[17]:
{1: ({'ssr_ftest': (20.47931250867985, 6.417180591997906e-06, 1823.0, 1),
'ssr_chi2test': (20.513014065194408, 5.922719066664915e-06, 1),
'lrtest': (20.398649686034332, 6.2874143889837596e-06, 1),
'params_ftest': (20.479312508695152, 6.417180591948046e-06, 1823.0, 1.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1329071d0>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x13297b990>,
array([[0., 1., 0.]])]),
2: ({'ssr_ftest': (11.217305932888081, 1.4393517271063477e-05, 1820.0, 2),
'ssr_chi2test': (22.496245414857967, 1.3031739092009448e-05, 2),
'lrtest': (22.358722057273553, 1.395934992576251e-05, 2),
'params_ftest': (11.217305932889026, 1.4393517271049108e-05, 1820.0, 2.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132979490>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132988210>,
array([[0., 0., 1., 0., 0.],
[0., 0., 0., 1., 0.]])]),
3: ({'ssr_ftest': (10.03932170550651, 1.4631471854955786e-06, 1817.0, 3),
'ssr_chi2test': (30.233994701448328, 1.2321700321788243e-06, 3),
'lrtest': (29.98615554979915, 1.3893420550221234e-06, 3),
'params_ftest': (10.039321705508376, 1.4631471854918153e-06, 1817.0, 3.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132937110>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132937e50>,
array([[0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 1., 0.]])]),
4: ({'ssr_ftest': (6.938798500217844, 1.5313121221361458e-05, 1814.0, 4),
'ssr_chi2test': (27.89289893251848, 1.3112092151438257e-05, 4),
'lrtest': (27.681662576447707, 1.4469768221310347e-05, 4),
'params_ftest': (6.938798500217278, 1.5313121221377616e-05, 1814.0, 4.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x13297ce50>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x13297e390>,
array([[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0.]])]),
5: ({'ssr_ftest': (5.6521512378289955, 3.533789083992374e-05, 1811.0, 5),
'ssr_chi2test': (28.432411803767064, 2.9956599752444827e-05, 5),
'lrtest': (28.212848370159918, 3.307219407698228e-05, 5),
'params_ftest': (5.652151237829557, 3.533789083988168e-05, 1811.0, 5.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x1328a2310>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132945710>,
array([[0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.]])])}
Caluclate the Covariance vallue for now if I can run a classic T-test or a Walsh t-test
In [18]:
plt.figure(figsize=(8, 6))
sns.heatmap(all_data_mean[['bitcoin', 'etherium']].cov(), annot=True)
plt.title('Heatmap Covariance Bitcoin - Etherium')
Out[18]:
Text(0.5, 1.0, 'Heatmap Covariance Bitcoin - Etherium')
Calculate the cointegration score for Bitcoin and Etherium
In [19]:
test_coint(all_data_mean, 'bitcoin', 'etherium')
Cointegration Test Statistic: -3.0553828789607036 P-value: 0.0976203440200703 No evidence of cointegration.
Out[19]:
(-3.0553828789607036, 0.0976203440200703, array([-3.90244781, -3.33947821, -3.04677349]))
Because the covaraince are not equal i made a Welch t-test
In [20]:
t_test(all_data_mean, 'bitcoin', 'etherium', equal_var=False)
There is a significant difference between the groups.
Out[20]:
(60.30652273568337, 0.0)
I compare the mean vallue of Bitcoin and Ehterium
In [21]:
all_data_mean['bitcoin'].mean()
Out[21]:
24124.186876242842
In [22]:
all_data_mean['etherium'].mean()
Out[22]:
1382.9994836761541
Analyse S&P/CAC/FTSE¶
Make the Granger Causality score beetwenn S&P/CAC4/FTSE 100
In [23]:
test_granger_causality(all_data_mean, 'sp', 'fts', max_lags=5)
Granger Causality Test Results: Lag 1: F-test: Statistic = 4.4752612222148604, P-value = 0.03452424709131348 Chi-squared test: Statistic = 4.482625886870178, P-value = 0.034241073415757405 Likelihood-ratio test: Statistic = 4.4771327023954655, P-value = 0.03435130546540045 Params F-test: Statistic = 4.475261222213212, P-value = 0.03452424709134593 Lag 2: F-test: Statistic = 4.200003686788619, P-value = 0.015141119632002667 Chi-squared test: Statistic = 8.423084316911241, P-value = 0.014823490530755106 Likelihood-ratio test: Statistic = 8.403706015677017, P-value = 0.014967815627883642 Params F-test: Statistic = 4.2000036867881185, P-value = 0.015141119632008341 Lag 3: F-test: Statistic = 8.699830484802078, P-value = 9.907916896910488e-06 Chi-squared test: Statistic = 26.20003985296476, P-value = 8.660473619241372e-06 Likelihood-ratio test: Statistic = 26.013653146786964, P-value = 9.474835430997154e-06 Params F-test: Statistic = 8.699830484801922, P-value = 9.907916896912548e-06 Lag 4: F-test: Statistic = 6.4403730897738605, P-value = 3.8198418902414176e-05 Chi-squared test: Statistic = 25.88930571699613, P-value = 3.331320372372934e-05 Likelihood-ratio test: Statistic = 25.707194574322784, P-value = 3.625068224360214e-05 Params F-test: Statistic = 6.440373089774692, P-value = 3.8198418902356775e-05 Lag 5: F-test: Statistic = 5.797266685456754, P-value = 2.5602537946846245e-05 Chi-squared test: Statistic = 29.162396192441207, P-value = 2.1547085647819246e-05 Likelihood-ratio test: Statistic = 28.931474606899428, P-value = 2.3916462740999062e-05 Params F-test: Statistic = 5.797266685455616, P-value = 2.5602537946911734e-05
/Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results warnings.warn(
Out[23]:
{1: ({'ssr_ftest': (4.4752612222148604, 0.03452424709131348, 1823.0, 1),
'ssr_chi2test': (4.482625886870178, 0.034241073415757405, 1),
'lrtest': (4.4771327023954655, 0.03435130546540045, 1),
'params_ftest': (4.475261222213212, 0.03452424709134593, 1823.0, 1.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a5ed90>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a47650>,
array([[0., 1., 0.]])]),
2: ({'ssr_ftest': (4.200003686788619, 0.015141119632002667, 1820.0, 2),
'ssr_chi2test': (8.423084316911241, 0.014823490530755106, 2),
'lrtest': (8.403706015677017, 0.014967815627883642, 2),
'params_ftest': (4.2000036867881185, 0.015141119632008341, 1820.0, 2.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a68650>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a6a650>,
array([[0., 0., 1., 0., 0.],
[0., 0., 0., 1., 0.]])]),
3: ({'ssr_ftest': (8.699830484802078, 9.907916896910488e-06, 1817.0, 3),
'ssr_chi2test': (26.20003985296476, 8.660473619241372e-06, 3),
'lrtest': (26.013653146786964, 9.474835430997154e-06, 3),
'params_ftest': (8.699830484801922, 9.907916896912548e-06, 1817.0, 3.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a69b90>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a6bdd0>,
array([[0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 1., 0.]])]),
4: ({'ssr_ftest': (6.4403730897738605, 3.8198418902414176e-05, 1814.0, 4),
'ssr_chi2test': (25.88930571699613, 3.331320372372934e-05, 4),
'lrtest': (25.707194574322784, 3.625068224360214e-05, 4),
'params_ftest': (6.440373089774692, 3.8198418902356775e-05, 1814.0, 4.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a69dd0>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a6b010>,
array([[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0.]])]),
5: ({'ssr_ftest': (5.797266685456754, 2.5602537946846245e-05, 1811.0, 5),
'ssr_chi2test': (29.162396192441207, 2.1547085647819246e-05, 5),
'lrtest': (28.931474606899428, 2.3916462740999062e-05, 5),
'params_ftest': (5.797266685455616, 2.5602537946911734e-05, 1811.0, 5.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a6b250>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a71290>,
array([[0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
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[0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.]])])}
In [24]:
test_granger_causality(all_data_mean, 'sp', 'cac', max_lags=5)
Granger Causality Test Results: Lag 1: F-test: Statistic = 0.006372709121573145, P-value = 0.9363818225358022 Chi-squared test: Statistic = 0.0063831963005993204, P-value = 0.9363208398303555 Likelihood-ratio test: Statistic = 0.006383185143931769, P-value = 0.9363208953618748 Params F-test: Statistic = 0.006372709120115911, P-value = 0.936381822542859 Lag 2: F-test: Statistic = 10.515415139707347, P-value = 2.88003150499978e-05 Chi-squared test: Statistic = 21.088607285676826, P-value = 2.634311406754158e-05 Likelihood-ratio test: Statistic = 20.967694200826372, P-value = 2.7984854624116913e-05 Params F-test: Statistic = 10.515415139708505, P-value = 2.8800315049965315e-05 Lag 3: F-test: Statistic = 15.280736532302713, P-value = 8.044615755909477e-10 Chi-squared test: Statistic = 46.01881689860233, P-value = 5.619478353774422e-10 Likelihood-ratio test: Statistic = 45.44788145766506, P-value = 7.431450464018619e-10 Params F-test: Statistic = 15.280736532302742, P-value = 8.044615755908848e-10 Lag 4: F-test: Statistic = 11.262497538874971, P-value = 4.992873681567404e-09 Chi-squared test: Statistic = 45.273501683283506, P-value = 3.4879624313124328e-09 Likelihood-ratio test: Statistic = 44.720464320038445, P-value = 4.5451865559232495e-09 Params F-test: Statistic = 11.262497538875659, P-value = 4.992873681561001e-09 Lag 5: F-test: Statistic = 9.954791992402805, P-value = 2.074994713517156e-09 Chi-squared test: Statistic = 50.07628661004393, P-value = 1.336868223077017e-09 Likelihood-ratio test: Statistic = 49.40048686202499, P-value = 1.83795015199251e-09 Params F-test: Statistic = 9.954791992402864, P-value = 2.0749947135167433e-09
/Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results warnings.warn(
Out[24]:
{1: ({'ssr_ftest': (0.006372709121573145, 0.9363818225358022, 1823.0, 1),
'ssr_chi2test': (0.0063831963005993204, 0.9363208398303555, 1),
'lrtest': (0.006383185143931769, 0.9363208953618748, 1),
'params_ftest': (0.006372709120115911, 0.936381822542859, 1823.0, 1.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a72150>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a72910>,
array([[0., 1., 0.]])]),
2: ({'ssr_ftest': (10.515415139707347, 2.88003150499978e-05, 1820.0, 2),
'ssr_chi2test': (21.088607285676826, 2.634311406754158e-05, 2),
'lrtest': (20.967694200826372, 2.7984854624116913e-05, 2),
'params_ftest': (10.515415139708505, 2.8800315049965315e-05, 1820.0, 2.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a71e10>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a71c90>,
array([[0., 0., 1., 0., 0.],
[0., 0., 0., 1., 0.]])]),
3: ({'ssr_ftest': (15.280736532302713, 8.044615755909477e-10, 1817.0, 3),
'ssr_chi2test': (46.01881689860233, 5.619478353774422e-10, 3),
'lrtest': (45.44788145766506, 7.431450464018619e-10, 3),
'params_ftest': (15.280736532302742, 8.044615755908848e-10, 1817.0, 3.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a719d0>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a71a50>,
array([[0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 1., 0.]])]),
4: ({'ssr_ftest': (11.262497538874971, 4.992873681567404e-09, 1814.0, 4),
'ssr_chi2test': (45.273501683283506, 3.4879624313124328e-09, 4),
'lrtest': (44.720464320038445, 4.5451865559232495e-09, 4),
'params_ftest': (11.262497538875659, 4.992873681561001e-09, 1814.0, 4.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a73810>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a73c10>,
array([[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0.]])]),
5: ({'ssr_ftest': (9.954791992402805, 2.074994713517156e-09, 1811.0, 5),
'ssr_chi2test': (50.07628661004393, 1.336868223077017e-09, 5),
'lrtest': (49.40048686202499, 1.83795015199251e-09, 5),
'params_ftest': (9.954791992402864, 2.0749947135167433e-09, 1811.0, 5.0)},
[<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a80450>,
<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x132a80790>,
array([[0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.]])])}
Create a heatmap with the correlation score and a line plot of the 3 vallue for see the evolution during the time.
In [25]:
plt.figure(figsize=(8, 6))
sns.heatmap(all_data_mean[['cac', 'fts','sp']].corr(), annot=True, cmap='coolwarm')
plt.title('Heatmap Correlation CAC 40/S&P/FTSE 100')
Out[25]:
Text(0.5, 1.0, 'Heatmap Correlation CAC 40/S&P/FTSE 100')
In [26]:
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(20, 15))
# Plot for 'Mean Price CAC 40'
all_data_mean['cac'].plot(ax=ax1,fontsize=16, color='blue')
ax1.set_title('Mean Price CAC 40')
ax1.legend()
# Plot for 'Mean Price FTSE 100'
all_data_mean['fts'].plot(ax=ax2, fontsize=16, color='orange')
ax2.set_title('Mean Price FTSE 100')
ax2.legend()
# Plot for 'Mean Price S&P 500'
all_data_mean['sp'].plot(ax=ax3,fontsize=16 , color='green')
ax3.set_title('Mean Price S&P 500')
ax3.legend()
Out[26]:
<matplotlib.legend.Legend at 0x132bbca10>
I have create a Correlation line wiht statsmodels for visualise the mean evolution of the correaltion score during time.
In [27]:
corr_ftse_cac = all_data_mean['fts'].rolling(30).corr(all_data_mean['cac'])
corr_ftse_sp = all_data_mean['fts'].rolling(30).corr(all_data_mean['sp'])
corr_cac_sp = all_data_mean['cac'].rolling(30).corr(all_data_mean['sp'])
fig = make_subplots(rows=3, cols=1)
corr_names = ["FTSE 100 vs CAC 40", "FTSE 100 vs S&P 500", "CAC 40 vs S&P 500"]
# Add traces and trendlines
for i, (corr, name) in enumerate(zip([corr_ftse_cac, corr_ftse_sp, corr_cac_sp], corr_names), 1):
fig.add_trace(go.Scatter(x=all_data_mean.index, y=corr, mode='lines', name=name), row=i, col=1)
fig.add_trace(go.Scatter(x=all_data_mean.index, y=calculate_ols_trendline(corr), mode='lines', name=f'{name} Trendline', line=dict(color='red')), row=i, col=1)
fig.update_layout(title='Rolling Correlations Over Time with OLS Trendlines', height=600, showlegend=True)
fig.update_xaxes(title_text='Date', row=3, col=1)
fig.update_yaxes(title_text='Correlation')
fig.show()
Like for bitcoint I have create a covarianse heatmap for now if i can use the clasic Anova test or the Welch variation.
In [28]:
plt.figure(figsize=(8, 6))
sns.heatmap(all_data_mean[['sp', 'fts','cac']].cov(), annot=True)
plt.title('Heatmap Covariance CAC 40/S&P/FTSE 100')
Out[28]:
Text(0.5, 1.0, 'Heatmap Covariance CAC 40/S&P/FTSE 100')
In [29]:
test_anova(all_data_mean, ['fts', 'cac','sp'],use_var='unequal',welch_correction=True)
ANOVA Test F-statistic: 20623.063222595832 P-value: 0.0 There is a significant difference between the groups.
Out[29]:
(20623.063222595832, 0.0)
To be sure of my Anova result I run three Welsh t-test to see if the result are the same
In [30]:
t_test(all_data_mean, 'sp', 'cac', equal_var=False)
There is a significant difference between the groups.
Out[30]:
(-115.00599433497874, 0.0)
In [31]:
t_test(all_data_mean, 'fts', 'cac', equal_var=False)
There is a significant difference between the groups.
Out[31]:
(80.04109944160375, 0.0)
In [32]:
t_test(all_data_mean, 'fts', 'sp', equal_var=False)
There is a significant difference between the groups.
Out[32]:
(224.8170799064647, 0.0)
I use the Levene test to compare the Variance betwen the group and validate my Covariance tab result
In [33]:
test_levene(all_data_mean, 'fts', 'cac')
Levene Test F-statistic: 157.07260627285507 P-value: 2.603245681724523e-35 There is a significant difference between the groups.
Out[33]:
(157.07260627285507, 2.603245681724523e-35)
In [34]:
test_levene(all_data_mean, 'fts', 'sp')
Levene Test F-statistic: 4.787779895620347 P-value: 0.02872550082027481 There is a significant difference between the groups.
Out[34]:
(4.787779895620347, 0.02872550082027481)
In [35]:
test_levene(all_data_mean, 'sp', 'cac')
Levene Test F-statistic: 340.6675502553561 P-value: 8.48238533801609e-73 There is a significant difference between the groups.
Out[35]:
(340.6675502553561, 8.48238533801609e-73)
Analyse all market together¶
For this part I have make scatter matrix for compare the varaition of all data together and a heat map for compare the correlation score.
In [36]:
sns.pairplot(all_data_mean, kind='reg', diag_kind= 'kde', plot_kws=dict(marker="+", line_kws={'color': 'red'}))
Out[36]:
<seaborn.axisgrid.PairGrid at 0x133501a50>
In [37]:
sns.pairplot(all_data_mean.pct_change(), kind='reg', diag_kind= 'kde', plot_kws=dict(marker="+", line_kws={'color': 'red'}))
Out[37]:
<seaborn.axisgrid.PairGrid at 0x136586c50>
In [38]:
plt.figure(figsize=(8, 6))
sns.heatmap(all_data_mean.corr(), annot=True, cmap='coolwarm')
plt.title('Heatmap Correlation')
Out[38]:
Text(0.5, 1.0, 'Heatmap Correlation')
In [39]:
plt.figure(figsize=(8, 6))
sns.heatmap(all_data_mean.pct_change().corr(), annot=True, cmap='coolwarm')
plt.title('Heatmap Correlation Percentage Variation')
Out[39]:
Text(0.5, 1.0, 'Heatmap Correlation Percentage Variation')
I make Cointegration test and Grange for compare all the data together and create a scatter plot matrix to visuliase the result
In [40]:
coint_matrix = test_all_pairs_coint(all_data_mean)
coint_matrix.sort_values(by='P-value')
Cointegration Test Statistic: -1.3676540416643885 P-value: 0.8083853324902368 No evidence of cointegration. Cointegration Test Statistic: -1.3081862910236866 P-value: 0.8272517835050854 No evidence of cointegration. Cointegration Test Statistic: -1.2369247376622878 P-value: 0.8479649886597967 No evidence of cointegration. Cointegration Test Statistic: -2.8199407444638216 P-value: 0.15942239182810208 No evidence of cointegration. Cointegration Test Statistic: -1.3339701044810772 P-value: 0.8192497775552554 No evidence of cointegration. Cointegration Test Statistic: -1.222632319803945 P-value: 0.8518745535910225 No evidence of cointegration. Cointegration Test Statistic: -1.531495279489717 P-value: 0.748917905786902 No evidence of cointegration. Cointegration Test Statistic: -3.0553828789607036 P-value: 0.0976203440200703 No evidence of cointegration. Cointegration Test Statistic: -1.944669111181519 P-value: 0.5571923696502682 No evidence of cointegration. Cointegration Test Statistic: -1.7949259357730085 P-value: 0.6321834911480554 No evidence of cointegration. Cointegration Test Statistic: -2.869771898342179 P-value: 0.1444908799944224 No evidence of cointegration. Cointegration Test Statistic: -2.387101735398906 P-value: 0.3309880036139313 No evidence of cointegration. Cointegration Test Statistic: -1.4147060534190505 P-value: 0.7924279671062884 No evidence of cointegration. Cointegration Test Statistic: -2.9980842792915006 P-value: 0.11066156178941328 No evidence of cointegration. Cointegration Test Statistic: -2.1384009367049948 P-value: 0.45631823803075483 No evidence of cointegration. Cointegration Test Statistic: -1.4106569919342273 P-value: 0.7938369775111298 No evidence of cointegration. Cointegration Test Statistic: -2.9526184810941474 P-value: 0.1219020413279614 No evidence of cointegration. Cointegration Test Statistic: -2.612074522957029 P-value: 0.23199324253726483 No evidence of cointegration. Cointegration Test Statistic: -2.8814001546353425 P-value: 0.14115313010195019 No evidence of cointegration. Cointegration Test Statistic: -3.220780871053438 P-value: 0.06652076426886551 No evidence of cointegration. Cointegration Test Statistic: -3.313328597109023 P-value: 0.05293022870087099 No evidence of cointegration. Cointegration Test Statistic: -2.5412552357031335 P-value: 0.26118354181058945 No evidence of cointegration. Cointegration Test Statistic: -2.6886720335495875 P-value: 0.20367929866742768 No evidence of cointegration. Cointegration Test Statistic: -2.4198396558945814 P-value: 0.3155169274534616 No evidence of cointegration. Cointegration Test Statistic: -3.124495326895609 P-value: 0.08348814008765171 No evidence of cointegration. Cointegration Test Statistic: -2.29324845781286 P-value: 0.3769265425915912 No evidence of cointegration. Cointegration Test Statistic: -2.1340895043688373 P-value: 0.4585659104168916 No evidence of cointegration. Cointegration Test Statistic: -1.4616755667052028 P-value: 0.7755926623518101 No evidence of cointegration. Cointegration Test Statistic: -1.913904321267141 P-value: 0.5729384036763813 No evidence of cointegration. Cointegration Test Statistic: -1.7453903061198746 P-value: 0.6558487611115338 No evidence of cointegration. Cointegration Test Statistic: -1.884489739694218 P-value: 0.5878523211374982 No evidence of cointegration. Cointegration Test Statistic: -3.0335118900829254 P-value: 0.10245299511428724 No evidence of cointegration. Cointegration Test Statistic: -3.0031632844551006 P-value: 0.10945549989677866 No evidence of cointegration. Cointegration Test Statistic: -1.2891558552514526 P-value: 0.8329839553983623 No evidence of cointegration. Cointegration Test Statistic: -1.192514683430678 P-value: 0.8598500923798182 No evidence of cointegration. Cointegration Test Statistic: -2.0434239548137616 P-value: 0.5059446733025528 No evidence of cointegration. Cointegration Test Statistic: -1.9445533332474105 P-value: 0.5572518775043169 No evidence of cointegration. Cointegration Test Statistic: -2.872820102105986 P-value: 0.14361059433534662 No evidence of cointegration. Cointegration Test Statistic: -2.9309700525501174 P-value: 0.1275390917727217 No evidence of cointegration. Cointegration Test Statistic: -1.393225892908496 P-value: 0.7998257898892177 No evidence of cointegration. Cointegration Test Statistic: -1.5065856745413173 P-value: 0.7586580902645625 No evidence of cointegration. Cointegration Test Statistic: -2.227417747748132 P-value: 0.4102730813268515 No evidence of cointegration.
Out[40]:
| Score | Test Statistic | P-value | Cointegrated | |
|---|---|---|---|---|
| 20 | fts/etherium | -3.313329 | 0.052930 | No |
| 19 | fts/bitcoin | -3.220781 | 0.066521 | No |
| 24 | pound/euro | -3.124495 | 0.083488 | No |
| 7 | bitcoin/etherium | -3.055383 | 0.097620 | No |
| 31 | sp/bitcoin | -3.033512 | 0.102453 | No |
| 32 | sp/etherium | -3.003163 | 0.109455 | No |
| 13 | etherium/bitcoin | -2.998084 | 0.110662 | No |
| 16 | etherium/sp | -2.952618 | 0.121902 | No |
| 38 | cac/etherium | -2.930970 | 0.127539 | No |
| 18 | fts/euro | -2.881400 | 0.141153 | No |
| 37 | cac/bitcoin | -2.872820 | 0.143611 | No |
| 10 | bitcoin/sp | -2.869772 | 0.144491 | No |
| 3 | euro/pound | -2.819941 | 0.159422 | No |
| 22 | fts/sp | -2.688672 | 0.203679 | No |
| 17 | etherium/cac | -2.612075 | 0.231993 | No |
| 21 | fts/pound | -2.541255 | 0.261184 | No |
| 23 | fts/cac | -2.419840 | 0.315517 | No |
| 11 | bitcoin/cac | -2.387102 | 0.330988 | No |
| 25 | pound/bitcoin | -2.293248 | 0.376927 | No |
| 41 | cac/sp | -2.227418 | 0.410273 | No |
| 14 | etherium/fts | -2.138401 | 0.456318 | No |
| 26 | pound/etherium | -2.134090 | 0.458566 | No |
| 35 | sp/cac | -2.043424 | 0.505945 | No |
| 8 | bitcoin/fts | -1.944669 | 0.557192 | No |
| 36 | cac/euro | -1.944553 | 0.557252 | No |
| 28 | pound/sp | -1.913904 | 0.572938 | No |
| 30 | sp/euro | -1.884490 | 0.587852 | No |
| 9 | bitcoin/pound | -1.794926 | 0.632183 | No |
| 29 | pound/cac | -1.745390 | 0.655849 | No |
| 6 | bitcoin/euro | -1.531495 | 0.748918 | No |
| 40 | cac/pound | -1.506586 | 0.758658 | No |
| 27 | pound/fts | -1.461676 | 0.775593 | No |
| 12 | etherium/euro | -1.414706 | 0.792428 | No |
| 15 | etherium/pound | -1.410657 | 0.793837 | No |
| 39 | cac/fts | -1.393226 | 0.799826 | No |
| 0 | euro/bitcoin | -1.367654 | 0.808385 | No |
| 4 | euro/sp | -1.333970 | 0.819250 | No |
| 1 | euro/etherium | -1.308186 | 0.827252 | No |
| 33 | sp/fts | -1.289156 | 0.832984 | No |
| 2 | euro/fts | -1.236925 | 0.847965 | No |
| 5 | euro/cac | -1.222632 | 0.851875 | No |
| 34 | sp/pound | -1.192515 | 0.859850 | No |
In [41]:
granger = test_all_pairs_granger_causality(all_data_mean, max_lags=5)
/Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: FutureWarning: verbose is deprecated since functions should not print results /Users/simongobin/anaconda3/lib/python3.11/site-packages/statsmodels/tsa/stattools.py:1488: 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In [42]:
fig= px.scatter(coint_matrix, x='Score',y='P-value', title="Cointvariance result")
fig.add_hline(y=0.05, line_dash="dash", line_color="red")
In [43]:
fig= px.scatter(granger, x='Causality Vallues',y='P-value', title="Granger causality result",color="Lag")
fig.add_hline(y=0.05, line_dash="dash", line_color="red")
I found a big cointegration score that mean a bit link between the Ehterium and FTSE 100 so i create a Plot line fro visulise this result
In [44]:
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(20, 15), sharex=False)
all_data_mean['etherium'].plot(ax=ax1, fontsize=16, color='blue')
ax1.set_ylabel('Mean Price Etherium')
ax1.set_title('Mean Prices of Etherium and FTSE 100 with Rolling Correlation')
all_data_mean['fts'].plot(ax=ax2, fontsize=16, color='orange')
ax2.set_ylabel('Mean Price FTS 100')
rolling_corr = all_data_mean['fts'].rolling(30).corr(all_data_mean['bitcoin'])
rolling_corr.plot(ax=ax3, fontsize=16, color='green')
ax3.set_ylabel('Rolling Correlation')
ax3.axhline(y=0, color='red', linestyle='--', linewidth=2)
ax1.legend(['Etherium Mean Price'])
ax2.legend(['FTSE 100 Mean Price'])
ax3.legend(['Rolling Correlation FTSE/BTC'])
plt.style.use('seaborn-v0_8-colorblind')
Majore variaiton¶
I have extract the 50 largest varaition in positive and 50 largest varaiton in negative and create a new datframe with this vallue
In [45]:
top_10_largest = all_data_mean.pct_change().apply(lambda col: col.nlargest(50))
top_10_smallest = all_data_mean.pct_change().apply(lambda col: col.nsmallest(50))
top10 = top_10_largest.copy()
top10_2=top_10_smallest.copy()
df_top = pd.concat([top10, top10_2])
I need to convert the new data frame in long fromat for create a historam with plotly
In [46]:
# Convert the DataFrame to a long format
df_long = df_top.reset_index().melt(id_vars='Date', var_name='Variable', value_name='Value')
# Create a scatter plot with a separate facet for each variable
fig = px.histogram(df_long, x='Date', y='Value', facet_row='Variable', title="Majore variation of price",nbins=260)
# Update layout for better readability
fig.update_layout(height=1200, showlegend=False)
fig.for_each_annotation(lambda a: a.update(text=a.text.split("=")[-1]))
fig.update_yaxes(matches=None)
fig.show()
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